Homework #7ΒΆ

Questions:

  1. Consider the process illustrated in this diagram:


    process system

    The process fluid has a density of \(\rho=\SI{9}{lb_{m}/gal}\). Assume that the pressure drop across the heat exchanger \(\Delta P_{he}\) is proportional to the volume flow rate squared, \(\dot{V}^{2}\), with \(\Delta P_{he} = 0\) at \(\dot{V} = 0\) and with \(\Delta P_{he} = \SI{30}{psi}\) at \(\dot{V} = \SI{200}{gal/min}\). The total difference in pressure between \(P_{1}\) and \(P_{2}\) is \(\SI{40}{psig}\), regardless of the flow rate.

    Consider three different options for the valve (valves 1, 2, and 3). These valves have different designs resulting in different volume flow rates at the same value of the valve position, \(L\). All three valves are designed so that the  \(\Delta P_{v} = \SI{10}{psi}\) when the flow rate \(\dot{V} = \SI{200}{gal/min}\).

    The designs have the following behavior:

    \[\dot{V} = 250 \sqrt{ \frac {\si{gal.lb_{m}}} {\si{psig.min^{2}}} } \cdot F\]

    where \(F\) is as follows

    • Valve 1: \(F = \sqrt{L \frac{\Delta P_{v}}{\rho}}\)

    • Valve 2: \(F = L \sqrt{\frac{\Delta P_{v}}{\rho}}\)

    • Valve 3: \(F = \left( 50^{L-1} \right) \sqrt{\frac{\Delta P_{v}}{\rho}}\)


    Use MATLAB to plot the flow rate through the system for different values of the valve position \((0 \le L \le 1)\) for each of the valve designs.

The following refer to the book Introduction to Chemical Engineering: Tools for Today and Tomorrow (5th Edition).

  1. Homework Problem 6 from Chapter 7 on page 122.

  2. Homework Problem 8 from Chapter 7 on page 122.

  3. Homework Problem 10 from Chapter 7 on page 123.

Review your responses to all of the homework questions before class so that you are prepared for the quiz on Tuesday!